A, B and C together can complete a piece of work in 30 minutes. A and B together can complete the same work in 50 minutes. C alone can complete the work in :
Q. A, B and C together can complete a piece of work in 30 minutes. A and B together can complete the same work in 50 minutes. C alone can complete the work in :
Answer: 75 minutes
Notes: Work done by (A + B + C) in 1 minute $latex = \frac{1}{30}&s=1$ Work done by (A + B) in 1 minute $latex = \frac{1}{50}&s=1$ ∴ Work done by C alone 1 minute $latex = \frac{1}{30}-\frac{1}{50}&s=1$ $latex = \frac{5-3}{150} = \frac{2}{150} = \frac{1}{75}&s=1$ ∴ C alone will complete the work in 75 minutes. Hence option [B] is correct answer.